An investigation by the Education Funding Agency (EFA) has found "serious failings" in the financial management of the school.

It also emerged that the headmaster had employed a number of his family members to work, including his brother as governor, sister as a senior teacher and even his own father acting as school bus driver.

The Department for Education (DfE) insisted a plan has been put in place to recover funds and that the school has been asked to address concerns urgently.

KSA was one of the first free schools to open in September 2011 and was praised by Prime Minister David Cameron on a visit last year.

It was judged to "require improvement" by Ofsted following an inspection in February.

BBC2's Newsnight programme said it had obtained the EFA report, which alleges that invoices were fabricated and that £86,000 of government funding has not been used for the purpose it was intended for.

It said the report claims Sajid Raza, the school principal who set up the academy, has admitted that some of the invoices submitted to the Department for Education for a lead in grant, were fabricated. It states that these invoices were created by the Trust to claim for rent they did not pay.

David Ward, MP for Bradford East, who sits on the Education Select committee, told the programme: "I have warned about this. Free schools are run by people who don't know enough about running schools. This is public money."

Interviewees for the programme said the school, which opened with more than £10million of public funds, according to the EFA report, was being run like a family business.

The draft report notes that Mr Raza employed many of his own family members at the school. His brother was on the board of governors, his sister was a senior teacher, his wife worked there and his father drove the school bus.

Daud Kahn, the school's former finance director, told Newsnight: "Sajid Raza would do a lot of things behind closed doors, he wouldn't get me involved or anybody else, and I don't know how much he was telling the governors, and even if he was telling them, the majority of them were all of their friends anyway, so they would back him up."

The report does not say if the family members were appointed through the usual processes or not.

The DfE said an inquiry was launched at the beginning of the year following allegations raised by a whistleblower about the way the school was being governed.

A planned visit to the Academy and concerns raised by accountants hired by the school itself led to the "forensic" investigation.

The EFA's final report found that out of a £182,933 grant made to the school before it opened, £86,335 had not been used for its intended purposes.

Invoices worth £59, 560 were not supported by any evidence of payments being made. This included "fabricated" invoices to the sum of £10,800 to cover rent for office accommodation.

A total of £26,775 had been over-paid against legitimate payments.

The report said: "Invoices have been submitted to the Department which have never been paid by the Trust."

It adds that it has been admitted that "some of the invoices submitted to the Department to support the claim for lead-in grant were fabricated invoices. These invoices were created by the Trust to claim for rent that they did not have to pay".

The DfE said that the police were informed of the allegations in April and no action was taken.

The school was issued with a warning notice in May and has since implemented an action plan to restructure its governing body, appoint an experienced finance director, overhaul its financial management systems, recruit new governors and pay back the money they owe.

"We informed the police who decided no further action was necessary. We required KSA to address these failings urgently.

"A plan is in place to recover funds and the school is undertaking its own investigation. Any necessary disciplinary action is a matter for the school."

He insisted that academies and free schools are subject to tougher financial accountability measures that other state schools.

He added: "Unfortunately no system of financial accountability for any school can guarantee it will prevent all wrongdoing.

"However, we take swift action when concerns are raised - academies and free schools cannot hide from their financial responsibilities and are held to account for their actions."

An undated statement from the chair of governors on the school's website says that since becoming aware of issues in a draft report, the governing body has taken "robust" action.

"The significant changes in membership has seen governors with expertise in finance, HR and education appointed to the governing body," it said.

"This now means that governors are able to effectively challenge the academy leadership, by having in place robust, accountable, systems and procedures which are constantly reviewed.

"This has led to significant improvements in governance which has been recognised by the EFA and in independent reviews.

"The governing body are committed to ensuring that all areas of the academy continue to improve to ensure outstanding outcomes for all our children."

A spokesman for the school told Newsnight: "The matters which you raise relate to issues regarding finance and governance two years ago during the Academy set-up process. We acknowledge there were poor governance issues during the start-up due to the pace of setting up the new school in two/three months. These have since been addressed with the support of external auditors and accountants. All payments received from DfE have been fully accounted for by the Academy, and any sums incorrectly claimed have been repaid."

The findings come at a time when free schools have been under the spotlight.

At the weekend, Deputy Prime Minister and Liberal Democrat leader Nick Clegg opened coalition dividing lines by publicly insisting that all teachers, including those at free schools, should be qualified.

Two free schools - the Al-Madinah School in Derby and Discovery New School in West Sussex - have been rated inadequate by Ofsted.

It was announced last month that Annaliese Briggs, who was appointed to run Pimlico Primary, a free school in central London, despite having little experience or teaching qualifications, was leaving the job just weeks after the school opened.

"Labour has long warned of the dangers that a lack of financial oversight and allowing unqualified teachers to teach in our classrooms on a permanent basis would cause.

"The case of KSA Free School further exposes David Cameron's weakness on school standards. It proves yet again that it is not possible for thousands of schools to be run directly from Whitehall and is further proof that this out-of-touch Government has no plan to deliver for all children."

The new development comes after it was reported that ministers approved plans to scrap checks for inexperienced headteachers hoping to run free schools, despite warnings from government officials that it could undermine a school's success.

Previously, school staff who did not have experience of leading a school were required to take part in an assessment centre to judge their capability.

But according to a leaked Department for Education (DfE) document seen by the BBC and the Guardian newspaper, ministers signed off plans to stop the requirement.

The DfE insisted that it was maintaining proper scrutiny of free school applications and that assessment centres "did not add value".

The document, which was drawn up by civil servants and sent to ministers for approval, puts forward ideas for cutting budgets in central areas of the department.

One of the suggestions is to ditch the "principal designate assessment centres".

But it also warns "Without PDACs, some free school projects may appoint inexperienced principal designates who are not suitable, which would significantly undermine the success of the school."

A single word comment on the suggestion from ministers says "stop", it was reported.

Christine Blower, general secretary of the National Union of Teachers, said: "It is now apparent that the DfE has been sitting on the report detailing financial irregularities at the Kings Science Academy since May and only released it late today once it became clear that the NUT had released to the press its own document outlining financial irregularities at the school.

"The catalogue of irregularities and what frankly points to fraud in the management of the school's finances acknowledged in the DfE's investigation report is a disgrace. This makes it very clear that the DfE lacks the proper procedures to manage and oversee its free schools programme. The audit investigation team deemed that the situation was so serious as to warrant investigation by the police.

"Michael Gove is himself personally responsible for this position. The public can no longer have confidence in him or his education policies.

"Problems around good governance, financial probity and standards of education are emerging in increasing numbers of free schools. The Government cannot continue to claim that these are isolated cases. These problems will continue to recur while we have a free school policy which allows groups to set up new schools and to run themselves without any accountability mechanisms.

"It is ironic that the Government has now asked the local authority to support the free school - a clear recognition of the educational expertise in local authorities. Free schools that are already opened should be brought within the local authority family of schools so they can be properly supervised in all their activities. The Government must end the approval of new schools by the free school route and must restore to local authorities the legal powers to open new maintained schools where places are needed. These schools must be locally accountable."